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Can you solve this 8-puzzle in 16 moves or less?

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1 Answer 1

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16 moves is the minimum possible. (I checked by computer, but solved it first without one.)

 P O S 
 L . S 
 E B I 
 
 P O S   P O S   P O S   P O S   P O S   . O S   O . S 
 L S .   L S I   L S I   L S I   . S I   P S I   P S I 
 E B I   E B .   E . B   . E B   L E B   L E B   L E B 
 
 O S S 
 P . I 
 L E B 
 
 O S S   O S S   O S S   O S .   O . S   . O S   P O S 
 P E I   P E I   P E .   P E S   P E S   P E S   . E S 
 L . B   L B .   L B I   L B I   L B I   L B I   L B I 
 
 P O S 
 E . S 
 L B I

Explanation:

By letting the blank go around 3/4 of the perimeter, you can cyclically shift 7 of the tiles, leaving one corner stationary. That corner tile is therefore jumped over by an adjacent tile, swapping two tiles relatively speaking.
By doing this twice, in opposite directions, on opposite corners, the effect is of swapping the two opposite corners with adjacent edge tiles, i.e. S-S and L-E.

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